More realistically, or at least for higher-mass planets,
radiation-hydrodynamical simulations have suggested the presence of
meridional circulation around an accreting planet:
motion from the upper layers of the protoplanetary disc towards the planet at its location,
where it has opened at least a partial gap
(e.g. [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]};
see also [15]}). Thanks to the exquisite sensitivity of ALMA,
[16]} provided the first observational evidence
for such a pattern over a scale of a few Hill radii in a young disc thought to contain accreting planets, HD 163296, and recently obtained a similar result for HD 169142 [17]}.
For such a geometry to hold, however, the gap opened by the planet needs to be not too wide,
and once higher masses have been reached, the large width of the gap
(\(\propto {M_{\mathrm {p}}}^{0.5}\) ; [18]}, but see also [19]}, who explore how time-dependent disc models lead to a different opening criterion than in equilibrium discs) should lead to accretion
from the CSD onto a circumplanetary disc (CPD),
and from this onto the planet.
This will hold especially in multiple-planet systems in which forming gas giants have opened a common gap [20]}. As [21]} point out, this might be a long phase of the accretion process,
over which a significant fraction of the planet mass could be assembled.
